Semiclassical Series from Path Integrals

Details Semiclassical Series from Path Integrals Semiclassical Series from Path Integrals

1999-03-08

arxiv.org/abs/quant-ph/9903028v2

Trends in Theoretical Physics II (AIP Conference Proceedings 484), edited by H. Falomir, R. E. Gamboa Saravi, and F. A. Schapo

Physics

Quantum Physics

18 pages, 4 figures. References updated

Scientific paper

10.1063/1.59667

We derive the semiclassical series for the partition function in Quantum Statistical Mechanics (QSM) from its path integral representation. Each term of the series is obtained explicitly from the (real) minima of the classical action. The method yields a simple derivation of the exact result for the harmonic oscillator, and an accurate estimate of ground-state energy and specific heat for a single-well quartic anharmonic oscillator. As QSM can be regarded as finite temperature field theory at a point, we make use of Feynman diagrams to illustrate the non-perturbative character of the series: it contains all powers of $\hbar$ and graphs with any number of loops; the usual perturbative series corresponds to a subset of the diagrams of the semiclassical series. We comment on the application of our results to other potentials, to correlation functions and to field theories in higher dimensions.

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